function F = sys1(x,eC,ell,theta,sigma,pi,rho,eta,i,M,A,B)
% partial equilibrium, given eC: eC = 1
q_star = 1;

q0A  = x(1);
q1A  = x(2);
q0B  = x(3);
q1Bn = x(4); % q0B
eNn  = x(5); % 1

a_CA_n = 1-ell;
a_NA_n = ell;
a_CB_n = 0;
a_NB_n = 0;
a_CA_d = 1-ell;
a_NA_d = ell;

F(1) = - i + ell*(1-(pi*a_CA_n+(1-pi)*a_CA_d)*theta/w(q1A,sigma,theta))*(mu(q0A,sigma)-1) ...
           + ell*   (pi*a_CA_n+(1-pi)*a_CA_d)*theta/w(q1A,sigma,theta) *(mu(q1A,sigma)-1);
F(2) = ell*(mu(q0B,sigma)-1) - i;

F(3) = - q1A  + min(q_star, q0A + ((eC*q0A+(1-eC)*q0B)/M*A/eC     - (1-theta)*(u(q1A,sigma) -u(q0A,sigma)))/theta);
F(4) = q0B - q1Bn;

F(5) = eNn - 1;

%=========================================================================
% subfunctions
%-------------------------------------------------------------------------
function u = u(q,sigma)
% CRRA utility: u(q)
if sigma < 1
    u = q.^(1-sigma)./(1-sigma);
elseif sigma == 1
    u = log(q);
end

function mu = mu(q,sigma)
% marginal utility: u'(q)
mu = q.^(-sigma);

function w = w(q,sigma,theta)
% w function in effective bargaining power
w = theta + (1-theta)*mu(q,sigma);
